Robust generalized observer design for uncertain one-sided Lipschitz systems

This paper develops a novel generalized observer design approach for the uncertain descriptor systems with one-sided Lipschitz nonlinearities, parametric uncertainties, and external perturbations. The nonlinearities, uncertainties, and external perturbations are considered both in input and output equations to consider a matter-of-fact observer design. A generalized structure for the observer is employed to deal with a large number of systems, considering both non-singular and singular systems. The proposed observer scheme is based on non-strict and strict linear matrix inequalities (LMIs), which are derived using the concepts of generalized Lyapunov theory, uncertainty bounds, quadratic inner-boundedness, one-sided Lipschitz condition, matrix transformations, and L₂ gain minimization criteria. The proposed state filtering approach is robust for disturbances with asymptotically stable estimation error dynamics under zero external perturbations and attenuation of disturbance effects to keep the estimation error within prescribed limits. In comparison to the conventional observer designs for the one-sided Lipschitz systems, the presented scheme is based on a generalized observer and can deal with parametric uncertainties. A numerical simulation example and an application example of spring-mass-damper system are provided to verify the effectiveness of the suggested filtering schemes.